Social Network Analysis: Introduzione all'analisi di reti sociali Michele Coscia Dipartimento di Informatica Università di Pisa www.di.unipi.it/~coscia
Piano Lezioni Introduzione Misure + Modelli di Social Network Graph Mining Applicazioni di ricerca su Social Network Software di Social Network Analysis (?)
Piano Lezioni Introduzione Il Grafo Esempi di Reti Sociali Reali Varianti di Grafo Storia della Social Network Analysis
Piano Lezioni Misure & Modelli di Social Network Grado e Degree Distribution Componenti connesse Shortest path, diametro e Small World Attacchi alla struttura della rete Omofilia e clustering Betweenness e Closeness Centrality Ego Networks
Piano Lezioni Misure & Modelli di Social Network Random graphs Configuration Model Markov Graphs Small World Model Preferential Attachment Model SIR/SIS Model
Piano Lezioni Graph Mining & Applicazioni Analisi Bibliografica Diffusione Informazione Expert Finding Recommendation Systems Viral Marketing
Piano Lezioni Software (forse!) Pajek http://vlado.fmf.uni-lj.si/pub/networks/pajek/ Ucinet http://www.analytictech.com/downloaduc6.htm ORA http://www.casos.cs.cmu.edu/projects/dynet/software.php Cytoscape http://www.cytoscape.org/ Webgraph http://webgraph.dsi.unimi.it/
Materiale M. E. J. Newman, The structure and function of complex networks www-personal.umich.edu/~mejn/courses/2004/cscs535/review.pdf Jiawei Han e Micheline Kamber, Data Mining: Concepts and Techniques (Capitolo 9.2: Social Network Analysis)
Introduction
The Graph Is a set of items, which we will call vertices With connections between them, called edges How can we represent this mathematical model?
The Graph (2) First representation: two relational tables One for nodes attributes, one for edges attributes The input format of most analytical programs Second representation: adjacency lists The computing format for most of the statistical procedures
The Graph (3) The Human readable format
Networks in real world: Society Nodes: individuals Links: social relationship (family/work/friendship/etc.)
Networks in real world: Actors Days of Thunder (1990) Far and Away (1992) Eyes Wide Shut (1999) Nodes: actors Links: cast jointly
Networks in real world: Sex Web Nodes: people (Females; Males) Links: sexual relationships
Networks in real world: Science Citation Networks Nodes: papers Links: citations Nodes: scientist (authors) Links: write paper together Scientific Coauthorship
Networks in real world: Communication The Earth is developing an electronic nervous system, a network with diverse nodes and links are -computers -routers -satellites -phone lines -TV cables -EM waves Communication networks: Many non-identical components with diverse connections between them.
Networks in real world: Biological Made of many non-identical elements connected by diverse interactions = Complex System
Networks in real world: Food Web Nodes: trophic species Links: trophic interactions
But... the graph is only the simplest tool for modeling 2 3 There are many variants that allow to capture different kind of relations 1 2 1 Different kinds of vertices and edges In a social network may be the nationality for people and the friendship/hate for relations) Edges can carry weights
Graph variants: Digraphs Graphs composed of directed edges are themselves called directed graphs or sometimes digraphs Example: the Web
Graph variants: Hypergraphs One can also have hyperedges: edges that join more than two vertices together Graphs containing such edges are called hypergraphs Could be used to indicate family ties in a social network For example n individuals connected to each other by virtue of belonging to the same immediate family could be represented by an n- edge joining them
Graph variants: Bipartite Bipartite graphs: graphs that contain vertices of two distinct types, with edges running only between unlike types So-called affiliation networks in which people are joined together by common membership of groups take this form, the two types of vertices representing the people and the groups
Social Network Analysis: The Beginning (1934) A social network is a set of people or groups of people with some pattern of contacts or interactions between them First example: Moreno's 1934 network of school children friendship
Social Network Analysis: Math Theorists Euler s celebrated 1735 solution of the Konigsberg bridge problem is often cited as the first true proof in the theory of network Rapoport (1957) stressed the importance of the degree distribution in networks of all kinds, not just social networks Another famous mathematical theorist: Paul Erdos (1959): the inventor of the random graph
Social Network Analysis: Sociological Experiments Small-world experiments of Milgram, 1967 No actual networks were reconstructed in these experiments, they tell us about network structure The experiments probed the distribution of path lengths in an acquaintance network by asking participants to pass a letter to one of their acquaintances in an attempt to get it to an assigned target individual This experiment was the origin of the popular concept of the six degrees of separation: everyone in the planet can reach everyone else by only contacting six people
Traditional Social Network Analysis: Problems Traditional social network studies often suffer from problems of inaccuracy, subjectivity and small sample size Data collection is usually carried out by querying participants directly using questionnaires or interviews These methods are labor-intensive and therefore limit the size of the network that can be observed Moreover are influenced by subjective biases on the part of respondents: how one respondent defines a friend, for example, could be quite different from how another does
Present Solutions...
Present Solutions!
Present Solutions Use the huge amount of data present in the World Wide Web Often already in a network form!
Basic Statistics of Classical Networks